Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.
Cube Rotation - dCode
Tag(s) : Fun/Miscellaneous
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Cube Rotation
Dice Rotations
Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.
Answers to Questions
How to list all rotations of the cube?
Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side) and so on to get all rotations.
Example:
| - | 1 | - |
| 5 | 4 | 2 |
| - | 6 | - |
| - | 3 | - |
How to count all possible rotations of a cube?
The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$ 6 \times 4 = 24 $$
Mathematically, how rotations of a cube are defined?
There are 4 types of rotation of a dice:
- Rotation according to the diagonals
- Rotation along the axis connecting the centers of 2 opposite faces
- Rotation along the axis connecting the centers of 2 opposite edges
- Identity rotation (original stationary state)
How to count all possible symmetries of a cube?
A cube whose faces are undifferentiated with 13 axes of symmetries:
- 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes
- 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes
- 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes
Source code
dCode retains ownership of the source code of the script Cube Rotation online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Cube Rotation script for offline use on PC, iPhone or Android, ask for price quote on contact page !
Questions / Comments
or 
